Solve for $x$ and $y$ using elimination. ${-2x-2y = -34}$ ${-5x+2y = -36}$
Answer: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Add the equations together. Notice that the terms $-2y$ and $2y$ cancel out. $-7x = -70$ $\dfrac{-7x}{{-7}} = \dfrac{-70}{{-7}}$ ${x = 10}$ Now that you know ${x = 10}$ , plug it back into $\thinspace {-2x-2y = -34}\thinspace$ to find $y$ ${-2}{(10)}{ - 2y = -34}$ $-20-2y = -34$ $-20{+20} - 2y = -34{+20}$ $-2y = -14$ $\dfrac{-2y}{{-2}} = \dfrac{-14}{{-2}}$ ${y = 7}$ You can also plug ${x = 10}$ into $\thinspace {-5x+2y = -36}\thinspace$ and get the same answer for $y$ : ${-5}{(10)}{ + 2y = -36}$ ${y = 7}$